Take b = 2.

b^(n-1) mod n = 1.

89 is prime.

b^((n-1)/89)-1 mod n = 35225, which is a unit, inverse 31036.

29 is prime.

b^((n-1)/29)-1 mod n = 20233, which is a unit, inverse 28348.

(29 * 89) divides n-1.

(29 * 89)^2 > n.

n is prime by Pocklington's theorem.